What we want to draw is the half closed interval:
I= [-5, 4) excluding 0,
as the union of 2 different intervals say a and b.
Let a be the interval containing the smallest value.
Then the smallest value of a is -5, and the largest possible value of a is 0, not included, if we want to write a as an interval, without "gaps", or "holes".
So a=[-5, 0)
similarly, b=(0, 4).
Answer: [-5, 4)=[-5, 0)∪(0, 4)
1) Circumference of Earth: Diameter x π → 12,800 x π = 40,212.39 km
2) time in Hour = distance/speed → distance = 40,212.39 and speed = 2 Mi/h
1st: convert miles into km : 1 mile = 1.609344 km and 2 miles = 3.218688 km
2nd: convert speed into km/h → speed = 3.218688 km/h
And time in hour = 40,212.39 / 3.218688 → time = 12,493 hours OR in days:
12,493 / 24 = 521 days (OR 104 weeks, including 2 days of rest)
The length of a curve <em>C</em> parameterized by a vector function <em>r</em><em>(t)</em> = <em>x(t)</em> i + <em>y(t)</em> j over an interval <em>a</em> ≤ <em>t</em> ≤ <em>b</em> is
In this case, we have
<em>x(t)</em> = exp(<em>t</em> ) + exp(-<em>t</em> ) ==> d<em>x</em>/d<em>t</em> = exp(<em>t</em> ) - exp(-<em>t</em> )
<em>y(t)</em> = 5 - 2<em>t</em> ==> d<em>y</em>/d<em>t</em> = -2
and [<em>a</em>, <em>b</em>] = [0, 2]. The length of the curve is then
